The Octagonal PETs
Seiten
2014
American Mathematical Society (Verlag)
978-1-4704-1522-8 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-1522-8 (ISBN)
A polytope exchange transformation is a (discontinuous) map from a polytope to itself that is a translation wherever it is defined. The 1-dimensional examples, interval exchange transformations, have been studied fruitfully for many years and have deep connections to other areas of mathematics, such as Teichmuller theory. This book introduces a general method for constructing polytope exchange transformations in higher dimensions and then studies the simplest example of the construction in detail. The simplest case is a 1-parameter family of polygon exchange transformations that turns out to be closely related to outer billiards on semi-regular octagons. The 1-parameter family admits a complete renormalization scheme, and this structure allows for a fairly complete analysis both of the system and of outer billiards on semi-regular octagons. The material in this book was discovered through computer experimentation. On the other hand, the proofs are traditional, except for a few rigorous computer-assisted calculations.
Richard Evan Schwartz, Brown University, Providence, RI, USA
Reihe/Serie | Mathematical Surveys and Monographs |
---|---|
Verlagsort | Providence |
Sprache | englisch |
Maße | 178 x 254 mm |
Gewicht | 456 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
ISBN-10 | 1-4704-1522-4 / 1470415224 |
ISBN-13 | 978-1-4704-1522-8 / 9781470415228 |
Zustand | Neuware |
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